On the Discrete Adaptive Posicast Controller

Abstract

In this paper, we present the discrete version of the Adaptive Posicast Controller (APC) that deals with parametric uncertainties in systems with input time-delays. The continuous-time APC is based on the Smith Predictor and Finite Spectrum Assignment with time-varying parameters adjusted online. Although the continuous-time APC showed dramatic performance improvements in experimental studies with internal combustion engines, the full benefits could not be realized since the finite integral term in the control law had to be approximated in computer implementation. It is shown in the literature that integral approximation in time-delay compensating controllers degrades the performance if care is not taken. In this work, we present a development of the APC in the discrete-time domain, eliminating the need for approximation. In essence, this paper attempts to present a unified development of the discrete-time APC for systems that are linear with known/unknown input time-delays. Performances of the continuous-time and discrete-time APC, as well as conventional Model Reference Adaptive Controller (MRAC) for linear systems with known time-delay are compared in simulation studies. It is shown that discrete-time APC outperforms its continuoustime counterpart and MRAC. Further simulations studies are also presented to show the performance of the design for systems with uncertain time-delay.

Control of Uncertain Sampled-Data Systems: An Adaptive Posicast Control Approach

“…As seen in Fig. 1, the proposed method provides convergence within a reasonable error bound around the desired trajectory as opposed to the approach in [37].…”

“…and, therefore, using the Key Technical Lemma, [31], [32], lim k →∞ β k z k + 1 = 0. Further, using the definition of β k given by (25), z k + 1 will converge to a bound of |ῡ k | ∈ O(τ + T ) • O(T ) and from the definition of z k , as k → ∞, the following stable error dynamics is achieved e k + 1 = Φ m e k +ῡ k (33) and, based on [37], lim k →∞ e k ≤ ∈ O(τ + T ) is guaranteed.…”

“…The approach incorporates a modified version of the disturbance observer method proposed by the author Abidi in [39]. Preliminary results of this work is presented in [36] without any stability analysis and a disturbance-free, ideal case where the timedelay is an integer multiple of the sampling interval is presented in [37] and [38].…”

Aplicaciones de Posicast en el diseño electrónico

“…Aplicaciones de Posicast en el diseño electrónico: una revisión conceptual y robustos (K. Abidi et al, 2016;Khalid Abidi et al, 2017;Khalid Abidi & Xu, 2015;Khalid Abidi & Yildiz, 2015;Khalid Abidi & Yildizt, 2011); diseño de controladores Posicast PID usando un algoritmo de búsqueda gravitacional (de Moura Oliveira et al, 2015); la aplicación de Posicast a plantas/procesos de orden fraccional (Gonzalez et al, 2013); la aplicación de Posicast/ IS de orden superior al problema del péndulo doble mediante un sistema de control basado en modelo de referencia (Fujioka & Singhose, 2018). También se realiza un interesante estudio sobre la aplicación de Posicast en casos en donde las condiciones iniciales son diferentes de cero (Esquivel & Tello, 2008).…”